1. Field of the Invention
The present invention relates to a method for suppressing the resonant effect between capacitors connected in parallel (shunt capacitors) by adjusting the length of the transmission lines between the shunt capacitors and, more particularly, to a method of adjusting the length of the transmission lines that applies to the π-filter circuit.
2. Description of Related Art
For the purpose of noise suppression or signal filtering, different filtering structures are required in designing circuits. In order to increase the capacitance or using the multi-stage structure, shunt capacitors are used in these filtering structures, and which require two or more capacitors connected in parallel. However, the finite series inductance of the capacitor mounted on PCB will limit the performance in some frequencies. Usually the equivalent circuit of a single capacitor is modeled as the series of a capacitor, resister and inductor. There exists the series resonance in the finite series inductance and the capacitance of the capacitor, which limits the performance of the shunt capacitors. In order to suppress the unwanted resonant effect, one method is using several identical capacitors. However, the bandwidth of this structure is still not wide enough.
FIG. 1 illustrates the equivalent circuit of a single capacitor. Its equivalent inductance and resistance are assumed to be 0.5 nH and 0.1Ω respectively. The inductance comes from the inner conductor of the capacitor, and the resistance is from the conductor loss of the element.
FIG. 2 shows the frequency responses of a single capacitor and two capacitors connected in parallel. A single capacitor with a capacitance of 400 pF, a series resistance of 0.1Ω, and a series inductance of 0.5 nH has the lowest impedance around the frequency of 350 MHz. This corresponds to the series resonance frequency formed by the series of the capacitance and the equivalent inductance. On the other hand, if two capacitors of capacitance 200 pF and 600 pF are connected in parallel, there exists two local minimum of impedance at 300 MHz and 500 MHz, which corresponds to the series resonant frequency of each capacitor. However, this structure creates an impedance peak at 400 MHz. This impedance peak comes from the parallel resonance between the capacitance in one capacitor and the inductance in the other capacitor. This resonant effect limits the performance of shunt capacitors in the frequency band of interest.
Further, to avoid parallel resonance while decreasing the impedance, it is common to have multiple identical capacitors connected in parallel as shown in FIG. 3. Though such method will not result in any impedance peak, which comes from the parallel resonance between the capacitors, the bandwidth will still not be wide enough.
From the above, conventional capacitors connected in parallel are not capable of either effectively suppressing resonant effect or increasing the bandwidth; therefore, it is desirable to come up with an improved method to overcome the above flaws.